The feet of the perpendiculars from any point N on the circumcircle of a triangle T to the sides of the triangle are collinear. The line of collinearity is called the Simson line of the point N for the triangle T

For a detailed description of the Simson line sl, use the routine detail (i.e., detail(sl))

Note that the routine only works if the vertices of triangle T are known.

The command with(geometry,SimsonLine) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{triangle}\left(T\,\left[\mathrm{point}\left(A\,-1\,0\right)\,\mathrm{point}\left(B\,1\,0\right)\,\mathrm{point}\left(C\,0\,1\right)\right]\right)\:$

$\mathrm{point}\left(N\,\frac{1}{\mathrm{sqrt}\left(2\right)}\,\frac{1}{\mathrm{sqrt}\left(2\right)}\right)\:$

$\mathrm{SimsonLine}\left(\mathrm{sl}\,N\,T\right)$

$\mathrm{sl}$

$\mathrm{detail}\left(\mathrm{sl}\right)$

assume that the names of the horizontal and vertical axes are _x and _y, respectively

$\begin{array}{ll}\text{name of the object}& \mathrm{sl}\\ \text{form of the object}& \mathrm{line2d}\\ \text{equation of the line}& \mathrm{\_x}\left(-\frac{1}{2}-\frac{\sqrt{2}}{2}\right)-\frac{\mathrm{\_y}}{2}+\frac{\left(\frac{\sqrt{2}}{2}+\frac{1}{2}\right)\sqrt{2}}{2}=0\end{array}$

$\mathrm{draw}\left(\left\{N\,T\,\mathrm{sl}\right\}\right)$